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# Trigonometric Identities

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ASSIGNMENT 6
7.4
Use an identity to write each expression as a single trig function value or as a single number.
14. 1 - 2 sin square 22 ½ degree
Express as a trig function of x
22. sin 4x
Write each expression as a sum or difference
44. sin 4x sin 5x
Write each expression as a product
46. cos 5x + cos 8x
Use a half-angle identity to find the exact value
54. tan 195 degrees
76 m>1 The Mach number is the ratio of the speed of the plane and the speed of the sound. Find theta if m = 5/4

7.5 Find the exact value of each real number y
20. y = arcsin (- square root 3/2)
28. y = sec^-1 (- square root 2)
Give the degree measure of theta
36. theta = arcsin (- square root 2/2)
Give each real number
52. y = arcos .44624593
Give the exact value of each expression
66. sec (sin^-1 (-1/5))
Find each value
80. sin (cos^-1 .25)

7.6 What is the appropriate technique to begin the solution of the equation
2. sin x + 2 =3
Solve each equation over the interval (0, 2pi)
20. 2 cos square x - square root 3 cos x = 0
Solve over the interval ( 0 degree, 360 degree)
28. cos square theta = sin square theta + 1
36. 4 cos square theta + 4 cos theta + 1
Determine all solutions in radians for x or degrees for theta to the nearest tenth
44. 2 cos square x + cos x = 1
62. 2square root 3 sin 2x = square root 3
Solve over the interval (0degrees, 360 degrees)
72. -2 cos 2theta = square root 3

7.7 Solve for x
6. 4y = sin x
Solve for exact solutions
24. 4pi + 4 tan^-1 y = pi
28. arctan x = arccos 5/13
34. arccos x + 2 arcsin square root 3/2 = pi/3